Mathematical model for crack arrest of a transversely cracked piezoelectromagnetic strip – Part I

A magnetic, electric and mechanical yield model is proposed for a cracked piezoelectromagnetic ceramic narrow strip. The strip is subjected to anti-plane mechanical and in-plane electric and magnetic loads, consequently the crack opens in self-similar fashion forming a magnetic, a saturation and a slide zone ahead each tip. These in turn are arrested by prescribing a magnetic, electric and mechanical load, respectively. Employing Fourier integral transform the problem reduces to the solution of three dual integral equations. The solution of dual integral equations is then expressed in terms of Fredholm integral equation of second kind. Expressions are derived for yield induction zone, slide-yield zone and saturation zone lengths, energy release rate. A case study is carried for BaTiO3–CoFe2O4 and results are presented graphically. It is shown that proposed model is capable of crack opening arrest under small-scale-yielding.